Math CentralQuandaries & Queries


Question from Elena:

After 9 weeks Mikayla has an average mark of 5 out of 10 in the weekly spelling tests. What is the minimum number of extra weeks now required to raise her average to 7?

Hi Elena,

Think about what the teacher did to calculate Milayla's average on the 9 tests. She found the sum of Milayla's marks on the 9 tests and divided by 9 to get 5. To say that mathematically let $S$ be the sum of her marks on the 9 tests then

\[\frac{S}{9} = 5.\]

Solve for $S.$

If she is to raise her average mark to 7 in the fewest possible weeks she will need to score 10 on each of the extra tests she writes. Suppose she writes tests for $w$ additional weeks and scores a 10 on each of these tests. What will be her total score on these additional tests? What will be he total score on all the tests she wrote, including the initial 9? This total divided by the number of weeks is 7. Solve for $w.$

Make sure you verify your answer.


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